Note

This documents the development version of NetworkX. Documentation for the current release can be found here.

networkx.algorithms.shortest_paths.weighted.negative_edge_cycle

negative_edge_cycle(G, weight='weight', heuristic=True)[source]

Returns True if there exists a negative edge cycle anywhere in G.

Parameters
  • G (NetworkX graph)

  • weight (string or function) – If this is a string, then edge weights will be accessed via the edge attribute with this key (that is, the weight of the edge joining u to v will be G.edges[u, v][weight]). If no such edge attribute exists, the weight of the edge is assumed to be one.

    If this is a function, the weight of an edge is the value returned by the function. The function must accept exactly three positional arguments: the two endpoints of an edge and the dictionary of edge attributes for that edge. The function must return a number.

  • heuristic (bool) – Determines whether to use a heuristic to early detect negative cycles at a negligible cost. In case of graphs with a negative cycle, the performance of detection increases by at least an order of magnitude.

Returns

negative_cycle – True if a negative edge cycle exists, otherwise False.

Return type

bool

Examples

>>> G = nx.cycle_graph(5, create_using=nx.DiGraph())
>>> print(nx.negative_edge_cycle(G))
False
>>> G[1][2]["weight"] = -7
>>> print(nx.negative_edge_cycle(G))
True

Notes

Edge weight attributes must be numerical. Distances are calculated as sums of weighted edges traversed.

This algorithm uses bellman_ford_predecessor_and_distance() but finds negative cycles on any component by first adding a new node connected to every node, and starting bellman_ford_predecessor_and_distance on that node. It then removes that extra node.